The strength of the Zeeman splitting induced by an applied magnetic field is an important factor for the realization of spin-resolved transport in mesoscopic devices. We measure the Zeeman splitting for a quantum point contact etched into a Ga0.25In0.75As quantum well, with the field oriented parallel to the transport direction. We observe an enhancement of the Lande g-factor from |g*|=3.8 +/- 0.2 for the third subband to |g*|=5.8 +/- 0.6 for the first subband, six times larger than in GaAs. We report subband spacings in excess of 10 meV, which facilitates quantum transport at higher temperatures.